# Imaginary Number Bases

## TL;DR

This paper extends the quarter-imaginary base system to all imaginary bases with zero real part and large imaginary magnitude, providing conversion methods, arithmetic operations, and potential applications.

## Contribution

It introduces a generalized imaginary number base system, including conversion algorithms, arithmetic procedures, and discusses possible practical uses.

## Key findings

- Provides conversion methods for imaginary bases
- Demonstrates addition, subtraction, multiplication, division in imaginary bases
- Suggests potential applications of imaginary number bases

## Abstract

An expansion upon Donald Kunth's quarter-imaginary base system is introduced to handle any imaginary number base where its real part is zero and the absolute value of its imaginary part is greater than one. A brief overview on number bases is given as well as conversion to both positive and negative bases. Additionally gives examples for addition, subtraction, multiplication for imaginary bases and adds a division method for imaginary bases as well as mentions possible uses.